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%I #13 Jan 11 2020 15:57:46
%S 0,1,4,65536,7625597484987
%N Perfect hyper-5 powers: a^^^b, where b <> 1.
%C a^^b (a to the hyper-4 power b) is the right associative power tower a^a^...^a^a of height b.
%C a^^^b (a to the hyper-5 power b) is the right associative hyper-4 power tower a^^a^^...^^a^^a of height b. a^^^-1 = 0, a^^^0 = 1;
%C We exclude b=1 because otherwise all natural numbers would be in the sequence.
%e Numbers satisfying the properties stated above:
%e 3^^^2 = 3^^3 = 3^3^3 = 3^27 = 7625597484987;
%e 2^^^3 = 2^^2^^2 = 2^^4 = 2^2^2^2 = 2^2^4 = 2^16 = 65536;
%e 1^^^4 = 1^^1^^1^^1 = 1.
%Y Cf. A001597, A257309.
%K nonn,bref
%O 1,3
%A _Natan Arie Consigli_, May 07 2015
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